OK. I've actually done this on quite a few tanks, including both of my current ones. I usually go 1" of dirt under 1.5-2" of sand.
The dirt does provide nutrients for quite a long time, actually. In my dirted tanks, with amazon swords, crypts, dwarf lilies, and other heavy root feeders, it takes several months to several years before I have to start adding root tabs.
The ammonia danger is blown out of proportion, IME. Sure, fresh dirt can release some ammonia. Very little of that makes it into the water column, and that clears up in a few weeks, about the time it takes your tank to cycle anyway. Saves me the trouble of adding ammonia. The early decomposition also seems to release a lot of CO2, which can give your plants an early boost if you're going low-tech.
Does dirt give any advantage over sand and chemical ferts? Not really. The real reason I do dirted tanks is that I enjoy the idea of making my tanks as close to nature as possible, and nature uses dirt, not root tabs. It always kind of amazes me that people are so scared to use something that doesn't come out of a bag from a store. Plain old dirt is safe and effective, as evidenced by pretty much every body of water in the world.
If you want to go all-natural, just dig up some soil from your back yard and go for it. If it has healthy plants and earthworms growing in it*, if it's at least a couple dozen meters from any major roadway, if it hasn't been sprayed with pesticides or chemical fertilizers, if you don't live in a mercury or uranium mine, it should work just fine. If you aren't sure or if you're just nervous about it, get some organic potting soil from your gardening center or hardware store (that's what I usually use, mostly because it's nice not having to dig out all the worms and grass roots). Commercially available soils will have a list of ingredients on the package. Avoid anything with chemical fertilizers, vermiculite/perlite, or anything that you can't pronounce or identify. You want some combination of sand, peat, loam, maybe a bit of compost (not much). That's it.
In an established, stocked tank with cycled media where you're going to have to add fish right away? It might be easier to go with sand and tabs, but you can still use dirt if you want to. If you do, plant it densely, light it brightly, keep close tabs on ammonia and nitrites for a couple months until the biology settles down, and be prepared to do big water changes if things go south. Your established media
should take care of any ammonia issues, and your plants will feast on all that lovely filth under the sand.
*plants and earthworms are signs of healthy soil. You don't necessarily want to put them in your aquarium, although if you miss one or two it won't really hurt anything unless you have toxic plants. A dead worm or a bit of grass root will just decompose along with all the other goodies in the soil.